> "Generate additional evidence at will" when applied to the "scientific fact that atoms exist" means that any new experiment that you design and perform will be compatible to that fact. There is no evidence whatsoever that atoms (at their "level of abstraction") do not exist.

You're describing certainty. This is a prediction, not reality. A new experiment you design and perform might not be compatible with the existence of atoms; that's the whole point of running experiments! (Of course, I have the same prediction; the proton-neutron-electron theory of atoms seems like a pretty solid one, at this point.)

Certainty does have interesting properties, from a Bayesian perspective: if you are certain of something, there is no finite amount of evidence that'll convince you otherwise. (Of course, humans aren't ideal Bayesian reasoners; you can usually provide enough evidence to convince a certain person otherwise, if they are actually wrong.)